Common Distance Metrics

In the KNN algorithm, it’s essential to identify the K data points closest to the data point of interest. To accomplish this, we employ distance measures. Here are some common distance metrics:

Euclidean Distance: is the Cartesian distance between two points in the plane or hyperplane, defined by the following formula:

d(x,y)=√(∑_(i=1)^n▒(x_i-y_i )^2 ),

where x=[x_1,…,x_n ]^T, y=[y_1,…,y_n ]^T

The Euclidean distance measures the straight-line distance between two points in space.

Manhattan Distance: is computed by summing the absolute differences between the coordinates of the points. It is employed when we are concerned with the total distance traveled by the object rather than just the displacement.

d(x,y)=∑_(i=1)^n▒|x_i-y_i | .

Minkowski Distance: serves as a generalization of both Euclidean Distance and Manhattan Distance. It is defined by the following formula:
d(x,y)=((x_i-y_i )^p )^(1/p)